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2002/2003 Extending some functions to functions satisfying condition \((A_3)\).
Zbigniew Grande
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Real Anal. Exchange 28(2): 573-578 (2002/2003).


A function \(f:\mathbb R \to \mathbb R\) satisfies the condition \(({\mathcal A}_3)\) if for each real \(r > 0\), for each \(x\) and for each set \(U \ni x\) belonging to the density topology there is an open interval \(I\) such that \(C(f) \supset I \cap U \neq \emptyset \) and \(f(U\cap I) \subset (f(x)-r,f(x)+r)\), where \(C(f)\) denotes the set of all continuity points of \(f\). In this article we investigate the sets \(A\) such that each almost continuous function may be extended from \(A\) to a function having property \(({\mathcal A}_3)\).


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Zbigniew Grande. "Extending some functions to functions satisfying condition \((A_3)\).." Real Anal. Exchange 28 (2) 573 - 578, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

MathSciNet: MR2010338

Primary: 26A05 , 26A15

Keywords: condition $({\cal A}_3)$ , continuity. , density topology , Extension‎

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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